Question:
Answer:
Here’s what a couple of Church Fathers believed about Peter being the Rock:
Augustine:
If the very order of episcopal succession is to be considered, how much more surely, truly, and safely do we number them [the bishops of Rome] from Peter himself, to whom, as to one representing the whole Church, the Lord said, ‘Upon this rock I will build my Church, and the gates of hell shall not conquer it.’ Peter was succeeded by Linus, Linus by Clement. . . . In this order of succession a Donatist bishop is not to be found (Letters 53:1:2 [A.D. 412]).
Cyprian:
The Lord says to Peter: “I say to you,” he says, “that you are Peter, and upon this rock I will build my Church, and the gates of hell will not overcome it. And to you I will give the keys of the kingdom of heaven” (Matt. 16:18–19). On him [Peter] he builds the Church, and to him he gives the command to feed the sheep (cf. John 21:17), and although he assigns a like power to all the apostles, yet he founded a single chair [cathedra], and he established by his own authority a source and an intrinsic reason for that unity. Indeed, the others were that also which Peter was [i.e., apostles], but a primacy is given to Peter, whereby it is made clear that there is but one Church and one chair. . . . If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he [should] desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church (The Unity of the Catholic Church 4; 1st edition [A.D. 251])?
This article, this article, and this one will give you a better understanding of the Greek used in Matthew 16:17-19.